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General Relativity and Gravitation

, Volume 26, Issue 10, pp 1011–1054 | Cite as

Metric-affine scale-covariant gravity

  • E. A. Poberii
Article

Abstract

We propose a gravitational theory based on the complete relaxing of Riemannian constraints (which force the connection to be symmetric and metric compatible) combined with the requirement of local conformal invariance. To reach this goal we generalize original Dirac's formalism of co-covariant calculus on spaces with arbitrary torsion and nonmetricity. The resulting gravitational theory turns out to be independent of the choice of measuring standards. Nevertheless there exists a mechanism of spontaneous gauge fixing through which all the masses in the universe could be generated. It is shown that field equations of the theory admit of a de Sitter solution with no cosmological constant, both in a vacuum case and in the presence of matter without proper hypermomentum. Various possible developments of the proposed theory are discussed in brief.

Keywords

Field Equation Cosmological Constant Differential Geometry Conformal Invariance Gravitational Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Adler, S. L. (1982).Rev. Mod. Phys. 54, 729.Google Scholar
  2. 2.
    Grib, A. A., Mamayev, S. G. and Mostepanenko, V. M. (1988).Vacuum Quantum Effects in Strong Fields (Energoatomizdat, Moscow, in Russian); Birrell, N. D., and Davies, P. C. W. (1982).Quantum fields in curved space (Cambridge University Press, Cambridge).Google Scholar
  3. 3.
    Brans, C., and Dicke, R. H. (1961).Phys. Rev. 124, 925.Google Scholar
  4. 4.
    Dicke, R. H. (1962).Phys. Rev. 125, 2163.Google Scholar
  5. 5.
    Ehlers, J., Pirani, F. A. E., and Schild, A. (1972). InGeneral Relativity, T. O'Raifertaigh, ed. (Oxford University Press, Oxford).Google Scholar
  6. 6.
    Heisenberg, W. (1938).Z. Phys. 110, 251.Google Scholar
  7. 7.
    Fulton, T., Rohrlich, F., and Witten, L. W. (1962).Rev. Mod. Phys. 34, 442.Google Scholar
  8. 8.
    Coleman, S., and Weinberg, E. (1973).Phys. Rev. D 7, 1888.Google Scholar
  9. 9.
    Minkowski, P. (1977).Phys. Lett. 71B, 419.Google Scholar
  10. 10.
    Niech, H. T. (1982).Phys. Lett. 88A, 388.Google Scholar
  11. 11.
    Zee, A. (1979).Phys. Rev. Lett. 42, 417.Google Scholar
  12. 12.
    Weyl, H. (1921).Raum, Zeit, Materie (4th ed., Springer-Verlag, Berlin).Google Scholar
  13. 13.
    Dirac, P. A. M. (1973).Proc. Roy. Soc. Lond. A333, 403.Google Scholar
  14. 14.
    Canuto, V., Adams, P. J., Hsieh, S.-H., and Tsiang, E. (1977).Phys. Rev. D 16, 1643.Google Scholar
  15. 15.
    Narlikar, J. V. (1979).Lectures on General Relativity and Cosmology (Macmillan, London).Google Scholar
  16. 16.
    Grib, A.A. (1992). Private communication.Google Scholar
  17. 17.
    Zee, A. (1983).Ann. Phys. (NY) 151, 431.Google Scholar
  18. 18.
    Mannheim, P. D. (1990).Gen. Rel. Grav. 22, 289.Google Scholar
  19. 19.
    Schouten, J. A. (1954).Ricci Calculus (2nd ed., Springer-Verlag, Berlin).Google Scholar
  20. 20.
    Einstein, A. (1953).The Meaning of Relativity (4th ed., Princeton University Press, Princeton).Google Scholar
  21. 21.
    Hammond, R. T. (1990).Class. Quant. Grav. 7, 2107.Google Scholar
  22. 22.
    Moffat, J. W. (1989).Phys. Rev. D 39, 474.Google Scholar
  23. 23.
    Hehl, F. W., von der Heyde, P., Kerlick, G. D. and Nester, J. M. (1976).Rev. Mod. Phys. 48, 393.Google Scholar
  24. 24.
    Hehl, F. W., Kerlick, G. D., and von der Heyde, P. (1976).Z. Naturf. 31a, 111, 524, 823.Google Scholar
  25. 25.
    Ne'eman, Y., and šija¯cki, Dj. (1979).Ann. Phys. (NY) 120, 292.Google Scholar
  26. 26.
    Rosen, N. (1982).Found. Phys. 12, 213.Google Scholar
  27. 27.
    Gregorash, D., and Papini, G. (1980).Nuovo Cimento 55B, 37;56B, 21.Google Scholar
  28. 28.
    Gasperini, M. (1988).Class. Quant. Grav. 5, 521.Google Scholar
  29. 29.
    Poberii, E. A. (1992). Preprint FL-030692, A.A. Friedmann Laboratory for Theoretical Physics.Google Scholar
  30. 30.
    Wood, W. R., and Papini, G. (1992).Phys. Rev. D 45, 3617.Google Scholar
  31. 31.
    Narlikar, J. V. (1985).Phys. Rev. D 32, 1928.Google Scholar
  32. 32.
    Obata, T., Oshima, H., and Chiba, J. (1981).Gen. Rel. Grav. 13, 3133.Google Scholar
  33. 33.
    Israelit, M., and Rosen, N. (1992).Found. Phys. 22, 555.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • E. A. Poberii
    • 1
  1. 1.Department of MathematicsA. A. Friedmann Laboratory for Theoretical PhysicsSt. PetersburgRussia

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